Tracking the Intangible: Quantifying Effort in NFL Running Backs
Image source: The Tower
Introduction
While athletes are often praised for “giving 100%,” what that entails remains poorly defined and difficult to measure objectively. Unlike physical traits such as endurance, strength, and agility, effort is intangible and often conflated with performance outcomes or inferred through subjective observation. Nevertheless, it is widely regarded as a crucial factor in athletic success, influencing both perceived competitiveness and in-game results. Developing a reliable, standardized method to evaluate effort could offer new insight into player behavior and decision-making.
This study focuses on running backs (RBs) in the NFL, a position characterized by short, high-intensity bursts of movement within clearly structured offensive plays. The nature of their role - frequent accelerations and heavy physical contact - make RBs a suitable candidate for analyzing exertion in a relatively controlled and consistent context.
Our approach builds on prior work deriving professional soccer players’ theoretical maximum acceleration capacity as a function of running speed in-situ1. To date, no comparable methodology has been applied to American football. By adapting it to RBs, we aim to isolate the measurable, physical component of effort, independent of tactical decisions or situational context.
The objective of this study is twofold: (1) to improve estimation of individual acceleration-speed (A-S) profiles using tracking data, and (2) to assess how frequently players operate near or exceed these limits as a proxy for effort.
Data
The data were obtained from the NFL Big Data Bowl 2025, an annual league-sponsored analytics competition that provides game, play, player, and tracking data recorded at 10 frames per second (nfl2025?). The dataset covers weeks 1-9 of the 2022 NFL season, comprising 136 games.
Pre-processing steps:
- Using the tracking data, we first standardized players’ positional coordinates and orientations so that all plays move from left to right, with the bottom-left corner of the field set as the “origin.”
- After merging the data, we filtered for running plays where the RB was the ball carrier and restricted the sample to RBs with at least 20 rushing attempts, yielding 69 players. Each observation corresponds to a single frame of tracking data.
- The tracking data provided only the magnitude of acceleration. To be able to differentiate between positive acceleration and negative acceleration (deceleration), we derived a variable for directional acceleration by multiplying the given magnitude of acceleration by the cosine of the angle of player motion. Speed and directional acceleration were converted to miles per hour (mph) and miles per hour per second (mph/s), respectively.
Methods
Motivation
Our initial approach was adapted from prior research building individual acceleration-speed (A-S) profiles of soccer players (Morin et al. 2021) For each RB, we plot the frame-level A-S profile based on the maximal acceleration they could generate for every possible running speed as follows:
Within a speed interval ranging between 3 mph and the RB’s maximal speed, the two maximal acceleration values attained for each 0.2 mph sub-intervals were selected. A first linear regression was fitted to these speed-acceleration points. Outlier points lying outside of the 95% confidence interval around the linear function were removed. A final linear regression was fitted to the remaining points, defining what we refer to as the “maximum acceleration frontier.”
To compute “effort” from the A-S profile, the regression line was first shifted downward by 0.25 units to include points sufficiently close to the estimated frontier. Effort was then defined as the percentage of a player’s points that fell above this relaxed threshold.
However, this approach has several limitations. First, it excludes points with speeds below 3 mph from the linear regression, effectively disregarding low-speed frames—even though effort may still be exerted at lower velocities. Second, the linear model extrapolates beyond the observed data, leading to unrealistic estimates of theoretical maximum speeds. Third, players with greater athletic ability may be disproportionately penalized. Because the frontier is estimated relative to each player’s own maximum accelerations, those with higher physical capacity face a stricter threshold, making their efforts appear less frequent with respect to their full potential. Finally, the model does not differentiate between acceleration and deceleration; all changes in velocity are treated equally, despite deceleration typically requiring less effort than acceleration3 and often reflecting tactical or situational constraints outside of the player’s control.
For every RB, we again examine the joint distribution of frame-level speed and acceleration. We define two approaches to evaluate effort as follows:
Metric #1: Quadratic Quantile Regression
Our main methodological approach to addressing this question centered around previous research that has explored soccer players reaching their theoretical max acceleration capacity for every running speed (Morin et al. 2021). Similarly, we adopted this framework by plotting an individual running back’s profile based on the maximal acceleration the running back could generate for every possible running speed as follows:
- Within a speed interval ranging between 3 mph and the RB’s maximal speed, the two maximal acceleration values attained for each 0.2 mph sub-intervals were selected.
- A first linear regression was fit to these speed-acceleration points.
- Outlier points lying outside of 95% confidence interval around the linear function were removed.
- A linear regression was fit to the remaining points.
This effort metric was derived by transforming final regression line downward by 0.25 units.
Effort = percentage of points above the transformed regression line
plotly
Metric #2: Quantile Generalized Additive Model
This metric quantifies how often a runnng back comes close to their maximal acceleration capacity.
Assumption of this effort metric: high acceleration and/or high speed movements are effortful.
For each running back, two regression models with adaptive spline bases were fitted to the 0.98 quantiles of positive and negative acceleration, respectively, both as functions of running speed. A vertical line at the 0.99 quantile of speed was also drawn.
This metric was derived by
[LATEX equation]
where di is the shortest distance from each point to its corresponding quantile regression line (either for positive or negative acceleration) or to the vertical line at the 0.99 quantile of speed.
- For points outside the quantile regression lines and/or the vertical line, the distance di was set to 0.
- For negative acceleration points, the effort score[change] was penalized with by a factor of 0.5 as deceleration is deemed less effortful.
Qgam
testing out a few players
Validation Model:
Top Running backs
Top 10
linear regression
Linear quantile regression for acceleration(mph/s) vs speed(mph)
Results
[Describe your results. This can include tables and plots showing your results, as well as text describing how your models worked and the appropriate interpretations of the relevant output. (Note: Don’t just write out the textbook interpretations of all model coefficients. Instead, interpret the output that is relevant for your question of interest that is framed in the introduction)]]
scatterplot
Discussion
[Give your conclusions and summarize what you have learned with regards to your question of interest. Are there any limitations with the approaches you used? What do you think are the next steps to follow-up your project?]
- AS profile framework didn’t translate into football (maybe it works for other sports where players don’t get tackled but just run at hand-off)
- there are many dependencies in NFL
- this is a productive place to start quantifying effort
- further research should look into taking into account other factors/variables
Appendix
Trying a different interactive layout
Acknowledgements
We are extremely grateful for all the guidance and support received throughout the duration of this project. Special thanks to our advisor, Sam Ventura from the Buffalo Sabres; program instructor, Quang Nguyen; program director, Ron Yurko; and program TAs Erin Franke, Leigh, Sara Colando, and Yuchen Chen.
References
Morin, Jean-Benoit, Yann Le Mat, Cristian Osgnach, Andrea Barnabò, Alessandro Pilati, Pierre Samozino, and Pietro E. di Prampero. 2021. “Individual Acceleration-Speed Profile in-Situ: A Proof of Concept in Professional Football Players.” Journal of Biomechanics 123: 110524. https://doi.org/https://doi.org/10.1016/j.jbiomech.2021.110524.